Calculation of electromotive force

Conductor moving within a uniform magnetic field B caused by a U-shaped magnet

Let’s look at the figure above. In it there is a straight conductor that moves with a certain speed inside a uniform magnetic field of induction B, originated by the U-shaped magnet. As we can see, the field generated by the magnet is uniform and perpendicular to the plane of the wire.

As electrons follow the motion of the straight conductor, they are subject to the magnetic force whose direction is determined by the right-hand rule or slap rule. Free electrons move to the lower end of the conductor in the figure; so that the other end is positive.

The charges at the ends give rise to an electric field E and the electrons are also subject to an electric force opposite the direction of the magnetic force. When these two forces balance, a potential difference is established between the ends of the wire. The ddp established between the ends of the conductor corresponds to the electromotive force which, in this case, is called the induced electromotive force.

When the circuit is closed, an electric current arises as a result of the ddp between the ends of the moving conductor, which crosses the uniform magnetic field B. The electric current that arises is called induced electric current.

Here’s how we can get the value of this electromotive force.

– the potential difference (U) is given by:

U=E.d

– in the equilibrium situation, we have:

mag = F el  like:

mag =Bqv  and   el =qE

We have:

Therefore, we can write:

ε=BLv

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